In a prior post we spoke about historical volatility using closing prices. Called Close-to-Close (C2C) Volatility measures the standard deviation of daily price changes. This blog takes us one step further and looks at how to calculate historical volatility as well as the assets range volatility & overnight action.

To review **CLOSE-TO-CLOSE (C2C)** Volatility, __read this blog first.__

This blog will cover different types of historical volatility used in the option markets and for risk management.

**RANGE VOLATILITY:** Takes into account the difference between the high & low for each trading day. Close to close volatility ignores intra-day moves.

**OVERNIGHT VOLATILITY:** Compares the opening price on day 1 versus the closing price on day zero. Overnight Vol is used so the trader can view overnight gaps quickly and compare overnight to other “normal” overnight vols. It gives traders a heads up that something is going on during non-trading hours effecting the following days opening price.

**MAX VOLATILITY:** Calculated using all three measures: Close to Close, Range & Overnight Volatility. The maximum measure is the “max vol” for that trading day. It will give traders a look at where the market is experiencing the highest volatility. If OVERNIGHT vol is the highest volatility, this shows something is happening during non-trading hours and the trader should evaluate this. These are all relative statements. As you will see as this series progresses we use ratio’s in order to compare figures more readily and utilize the results more effectively.

### COMPARING DIFFERENT VOLATILITY A CANDLESTICK CHART

This 3 day candlestick chart is to illustrate why these three volatility measures could be different. For example:

The range (length of the candle) relative to the closing price for each day.

The closing price is shown as the bold horizontal line to the right of the candle

The opening price is shown as the blue horizontal line to the left of the candle

**CALCULATING C2C, RANGE & OVERNIGHT VOLATILITY**

**10 DAY CLOSE-TO-CLOSE VOLATILITY **

The following show how C2C volatility is calculated. From Column C to column H the same data is used; Take note from column I to Q for the manner in which each measure adjusts the days price action.

Columns C, D, E, F, G, H: OPEN, HIGH, LOW, CLOSE, VOLUME, ADJUSTED CLOSING PRICE (price adjusted for splits and divs)

*Adjusted close (price inclusive of splits, etc.) is always used for equities, but can be used for other assets whose value changes due to distribution by the underlying asset. *

Column I: calculates the THE DAILY CHANGE, RANGE or OVERNIGHT NUMBERS

Column J: Calculates the Natural Logarithm of the percentage Change, Range or overnight move

Columns K to Q shows all of the calculations for illustration purposes.

*N.B.: STDEV is used for the interim calculations, then annualized [multiplied by SQRT (252)] *

**TABLE 2 – shows the calculations for close to close volatility**

*N.B.: STDEV (J2:J2) = ~1.492%. One standard deviation, using normal distribution says that 68.3% of all occurrences take within 1 standard deviation from the mean. *

To review the daily probability statement using close-to-close (C2C) volatility would be:

*ONE STANDARD DEVIATION (68.3%): **2 out of 3 days (on average, over time) Apple Computer close up or down 1.492% or less. 1 out of 3 days, AAPL closes up or down MORE THAN 1.49%*

TWO STANDARD DEVIATIONS 95.4%: 19 out of 20 days (on average over time) ~ 2.98%; 1 out of 20 days the asset should trade up or down MORE THAN 2.98%

THREE STANDARD DEVIATIONS (99.7%): 299 out of 300 days (on average, over time) ~4.46%, 1 out of 300 days the asset should close up or down MORE THAN 4.46%

*The exact numbers for up & down differ – as the calculation uses the exponent e. **If you prefer to use that level of precision, there is an ASSET PROBABILITY RANGE CALCULATOR you can find, here. *

**TABLE 3 – Calculates RANGE volatility. Column J shows the LN of the daily percentage range**

The 11 day range volatility is 17.77% per annum or 1.119% per day (i.e., 2 out of 3 days, the range is expected to be within 1.119%, 1 out of 3 days the range is expected to be MORE THAN 1.119%)

**TABLE 4 – Calculate OVERNIGHT volatility. Compares OPEN (DAY2) versus the CLOSE (DAY 0)**

The 11 day overnight Volatility is .851% per day or 13.51% annualized. While one observation may be sufficient for educational purposes, in reality we would create a time series, continuing to add the current daily data and delete the most distant days data from the calculation.

**TABLE 5 shows 10 day historical vol rolling forward from 9/25/15 – 9/29/15**

DAY ONE: 9/25/15 DATA = 9/11 – 9/25/15

DAY TWO: 9/28/15 DATA= 9/14 – 9/28/15

DAY THREE: 9/29 DATA = 9/15 – 9/29/15

## SUMMARY

So far this series has covered: Close-to-Close Volatility (C2C), Range & Overnight Volatility. Our next installment will cover Implied Volatility & Event (Earnings, Seasons, etc.) Volatility prior to delving into strategy and how these numbers are used by the various market participants.

In the meantime, if you have any questions, please press the button on the right sidebar and we’ll revert as soon as possible with your answer.

## OTHER RESOURCES

There are great volatility resources on the internet so you don’t have to calculate everything yourself. Indeed, your focus should be on your risk management levels. I like **www.ivolatility.com. **They provide a snapshot for each asset free of charge. Full Disclosure: I use pay portions of the site as well.

When I want to get a quick historical volatility chart, I use asset price data from **www.yahoo.com.** They provide the all important ADJUSTED close in addition to the open, high, low, close & volume.